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How Can We Maximize Phylogenetic Diversity? Parameterized Approaches for Networks

Authors Mark Jones , Jannik Schestag

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Author Details

Mark Jones
  • TU Delft, The Netherlands
Jannik Schestag
  • TU Delft, The Netherlands
  • Friedrich-Schiller-Universität Jena, Germany

Funding

  • Jones, Mark: Partially supported by Netherlands Organisation for Scientific Research (NWO) grant OCENW.KLEIN.125.
  • Schestag, Jannik: Supported by the German Academic Exchange Service (DAAD), project 57556279.

Cite AsGet BibTex

Mark Jones and Jannik Schestag. How Can We Maximize Phylogenetic Diversity? Parameterized Approaches for Networks. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 30:1-30:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.IPEC.2023.30

Abstract

Phylogenetic Diversity (PD) is a measure of the overall biodiversity of a set of present-day species (taxa) within a phylogenetic tree. We consider an extension of PD to phylogenetic networks. Given a phylogenetic network with weighted edges and a subset S of leaves, the all-paths phylogenetic diversity of S is the summed weight of all edges on a path from the root to some leaf in S. The problem of finding a bounded-size set S that maximizes this measure is polynomial-time solvable on trees, but NP-hard on networks. We study the latter from a parameterized perspective. While this problem is W[2]-hard with respect to the size of S (and W[1]-hard with respect to the size of the complement of S), we show that it is FPT with respect to several other parameters, including the phylogenetic diversity of S, the acceptable loss of phylogenetic diversity, the number of reticulations in the network, and the treewidth of the underlying graph.

Subject Classification

ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
  • Theory of computation → W hierarchy
  • Applied computing → Bioinformatics
Keywords
  • Phylogenetic Networks
  • Phylogenetic Diversity
  • Parameterized Complexity
  • W-hierarchy
  • FPT algorithms

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